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Greg buys bananas and apples for a total price of $2.45. How

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Greg buys bananas and apples for a total price of $2.45. How

Post Sun Dec 03, 2017 3:18 pm
Greg buys bananas and apples for a total price of $2.45. How many pounds of fruit did Greg buy?

(1) The price of each pound of bananas is $0.49
(2) The price of each pound of apples is $0.98

What's the best way to determine whether statement 1 is sufficient? Can any experts help?

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Post Thu Jan 11, 2018 4:37 pm
ardz24 wrote:
Greg buys bananas and apples for a total price of $2.45. How many pounds of fruit did Greg buy?

(1) The price of each pound of bananas is $0.49
(2) The price of each pound of apples is $0.98
We can let b = the number of pounds of bananas he bought and a = the number of pounds of apples he bought, and we know the total spent is $2.45.

Statement One Alone:

The price of each pound of bananas is $0.49.

Since we do not know anything about the price of apples, statement one alone is not sufficient to answer the question.

Statement Two Alone:

The price of each pound of apples is $0.98.

Since we do not know anything about the price of bananas, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we can create the equation:

0.49b + 0.98a = 2.45

49b + 98a = 245

49(b + 2a) = 245

b + 2a = 5

Since we cannot determine a unique value of a or b (for example, a could be 2 and b could be 1 OR a could be 1 and b could be 3), the statements together are not sufficient.

Answer: E

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GMAT/MBA Expert

Post Mon Dec 04, 2017 4:02 pm
ardz24 wrote:
Greg buys bananas and apples for a total price of $2.45. How many pounds of fruit did Greg buy?

(1) The price of each pound of bananas is $0.49
(2) The price of each pound of apples is $0.98
Statements combined:
Let b = the number of pounds of bananas and a = the number of pounds of apples.
Since 1 pound of bananas costs 49 cents, 1 pound of apples costs 98 cents, and the total cost is 245 cents, we get:
49b + 98a = 245.
Since b and a are not constrained to integer values -- it is possible to buy 1/2 pound of bananas or 2.1 pounds of apples -- the equation above has an infinite number of solutions.
Thus, the total weight -- the value of b+a -- cannot be determined.

The correct answer is E.

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GMAT/MBA Expert

Post Mon Dec 04, 2017 11:53 am
Hi ardz24,

We're told that Greg buys bananas and apples for a total price of $2.45. We're asked for the number of pounds of fruit that Greg bought.

1) The price of each pound of bananas is $0.49

Fact 1 tells us nothing about the cost of a pound of apples so the answer to the question could vary.
Fact 1 is SUFFICIENT

2) The price of each pound of apples is $0.98

Fact 2 tells us nothing about the cost of a pound of bananas so the answer to the question could vary.
Fact 2 is INSUFFICIENT

Combined, we know...
-The total money spent is $2.45
-The price of each pound of bananas is $0.49
-The price of each pound of apples is $0.98

Notice how the price of a pound of apples is EXACTLY DOUBLE the price of a pound of bananas and $2.45 is EXACTLY 5 times $0.49. You can use this pattern to your advantage (or simply do a bit of brute-force arithmetic) and prove that there are 2 answers to the question.
IF there are...
3 pounds of bananas and 1 pound of apples, then the answer to the question is 4
1 pound of bananas and 2 pound of apples, then the answer to the question is 3
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

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